Brownian motion of a drop with hysteresis dissipation

Small water drops placed on a low-energy substrate with a slight tilt were vibrated parallel to the support with bands of Gaussian white noise of different powers. The drops drifted downward on the inclined support accompanied with random forward and backward movements. For a hysteresis free surface, the drift velocity should only be the product of the component of the gravitational acceleration and the Langevin relaxation time, being independent of the power of noise. On the other hand, in the presence of hysteresis, as is the case here, the drift velocity depends strongly on the power of the noise. This result illustrates the role of hysteresis in the drifted motion of drops on a surface subjected to vibration, which has important bearings on various forms of work fluctuation relations.     

Shape relaxation of an elongated viscous drop

The shape relaxation of a distorted viscous drop suspended in a quiescent immiscible liquid is analyzed in the creeping flow limit. The shape of the drop is axisymmetric, but otherwise arbitrary. The relaxation process is assumed to be driven by a constant interfacial tension and rate-limited by the Newtonian viscosities of the dispersed and continuous phases. For analysis, a least squares technique is developed which, compared to the more common boundary integral methods, is simpler to implement and especially suited for systems where one liquid is much more viscous than the other (i.e., when the viscosity ratio lambda, defined as the ratio of the dispersed to continuous phase viscosities, approaches either zero or infinity). To demonstrate the validity of the proposed least squares technique, its results are shown to agree well with boundary integral calculations for moderate values of lambda, and with experimental data when lambda is much larger than unity (approximately 10(6)). Predictions at infinite viscosity ratio--the regime in which the least squares technique is most useful--are then used to evaluate interfacial tensions associated with a system of practical importance, namely, the dispersion of heavy crude oil in an aqueous environment. This amounts to a novel and accurate technique for determining interfacial tensions--especially those of low values (1 mN/m or less)--between density-matched liquids where at least one of the phases is highly viscous. The experimental part of this study involves the use of suction pipettes to manipulate the shapes of individual micrometer-sized droplets, thus avoiding the need for complex flow-generating devices to create drop deformations.     

Experimental observation of oscillatory effects on the relaxation of a sheared liquid drop

This work deals with the experimental observation of the shape oscillations followed by a viscous liquid drop immersed in another viscous fluid matrix when retracting from a deformed state into the spherical shape under the action of interfacial forces. The droplet is firstly deformed into an ellipsoidal shape by a shear flow and later allowed to recover the equilibrium shape after cessation of the flow. It is observed that such an oscillatory process occurs for a wide range of viscosity ratios and it may be described by a dampened oscillation. Viscous components dominate the drop retraction, just allowing few oscillations. The dampening factor, frequency and amplitude of the oscillations are affected by the drop viscosity. Frequencies and amplitudes are also influenced by the initial drop deformation.     

Molecular dissipation phenomena of nanoscopic friction in the heterogeneous relaxation regime of a glass former

Nanoscale sliding friction involving a polystyrene melt near its glass transition temperature Tg (373 K) exhibited dissipation phenomena that provide insight into the underlying molecular relaxation processes. A dissipative length scale that shows significant parallelism with the size of cooperatively rearranging regions (CRRs) could be experimentally deduced from friction-velocity isotherms, combined with dielectric loss analysis. Upon cooling to approximately 10 K above Tg, the dissipation length Xd grew from a segmental scale of approximately 3 A to 2.1 nm, following a power-law relationship with the reduced temperature Xd approximately TR-phi. The resulting phi=1.89+/-0.08 is consistent with growth predictions for the length scale of CRRs in the heterogeneous regime of fragile glass formers. Deviations from the power-law behavior closer to Tg suggest that long-range processes, e.g., the normal mode or ultraslow Fischer modes, may couple with the alpha relaxation, leading to energy dissipation in domains of tens of nanometers.     

Stress relaxation behaviour of dipalmitoyl phosphatidylcholine monolayers spread on the surface of a pendant drop

Dipalmitoyl phosphatidylcholine (DPPC) monolayers were characterised by surface pressure/area isotherms (π/A) and surface dilational rheological parameters at temperatures 20–40°C. The methods used were the Langmuir trough and the pendant drop micro-film balance. The latter allows accurate measurements at higher temperatures and transient drop deformation. Stable DPPC monolayers were found only for low surface pressures, π<15 mN m⁻¹. At higher monolayer compression π decreases over a long time, mainly caused by molecular rearrangement processes in the monolayer starting in the coexisting region. At π>25 mN m⁻¹ and 20°C relaxation experiments give evident of rupturing, brittle monolayer structures. At higher temperatures the monolayers became more fluid-like. π/A-isotherms determined by using both methods principally agree with each other, but show also remarkable differences, which cannot be explained so far satisfactory. Transient drop relaxation experiments were analysed for the short time range (600 s). At 20°C the dilational modulus (_r) and the surface dilational viscosity (ξ_r) passes a stationary maximum at 0.54 nm² molecule⁻¹ and increase strongly at higher surface coverage, thus indicating crystalline monolayer structure. Increasing temperature from 20 to 30°C causes a rapid decrease of _r and ξ_r and a shift of the stationary maximum to lower surface coverage. No evidence for crystalline structure is found. Further increase of temperature causes _r and ξ_r increase again. This increase is caused by a rising relaxation time, while the elasticity does not change in the same manner. Such intermediate decrease of _r and ξ_r in the range 30–40°C appears to be unusual and can be interpreted as a consequence of strong DPPC interactions and strongly pronounced retardation of monolayer deformation. The study is discussed in connection to the physiology of breathing. For pulmonary surfactants the observed behaviour seems to be understandable. It is however interesting that such complex behaviour is observed for monolayers consisting of DPPC only.     

Logarithmic relaxation in a kinetically constrained model

We present Monte Carlo simulations on a coarse-grained model for relaxation in binary mixtures. The liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting, respectively, unexcited and excited local states in a mobility field. Change in local mobility (spin flip) is permitted according to kinetic constraints determined by the mobilities of neighboring cells. We introduce two types of cells ("fast" and "slow") with very different rates for spin flip. Fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in dynamic correlators by changing temperature or composition. At intermediate state points logarithmic relaxation is observed over three time decades. These results display striking analogies with dynamic correlators reported in recent simulations on polymer blends.     

On the importance of the classically forbidden region in calculations of the relaxation rate for high-frequency vibrations: a model calculation

The quantum mechanical relaxation rate for a high-frequency vibrational mode is evaluated for a one-dimensional model system having two diatomic molecules involved in a collinear collision. The thermally averaged rate is obtained as an integral over energies for the relative translation of the two molecules. These calculations show that energies several times K(B)T make the largest contributions to the rate. Several orders of magnitude of cancellation due to phase interference is found in the evaluation of the coupling matrix elements between the initial and final states, and this is one of the main factors leading to the very small value for the relaxation rate. The region near the classical turning point in the relative translational motion of the colliding molecules dominates the calculation of the contribution to the rate at each energy. Calculations using low-order expansions of the translational potential energy and the interstate coupling about this turning point provide good approximations to the exact quantum mechanical rate. This suggests a possible method for performing calculations of the rate by means of realistic simulations of liquid systems.     

Aging in a free-energy landscape model for glassy relaxation

The aging properties of a simple free-energy landscape model for the primary relaxation in supercooled liquids are investigated. The intermediate scattering function and the rotational correlation functions are calculated for the generic situation of a quench from a high temperature to below the glass transition temperature. It is found that the reequilibration of molecular orientations takes longer than for translational degrees of freedom. The time scale for reequilibration is determined by that of the primary relaxation as an intrinsic property of the model.     

Investigations of drop impact on dry walls with a lattice-Boltzmann model

In this work, axisymmetric computations of drop impingement on dry walls are presented. The two-phase model employed is an axisymmetric lattice-Boltzmann model. Computations are performed in the parametric range of Weber number We of 7 to 8770, Ohnesorge number Oh of 0.02 to 0.137, and drop-wall equilibrium contact angle theta(eq) of 35 degrees to 150 degrees . Deposition and rebound outcomes are reported. In deposition, the different stages of drop evolution including spread, recoil and equilibration are reproduced and studied. Comparisons made with experimentally reported data of temporal evolution of the spread factor and the dynamic evolution of the contact angle show good agreement. Rebound is observed on non-wetting surfaces. The transition between deposition and rebound is shown to be influenced by the impact We, Oh, and advancing and receding static contact angles. Apart from impingement outcomes, the influence of We and Oh on the dynamic contact angle is investigated.     

On the interpretation of dielectric relaxation in nematogens

The dielectric relaxation in the isotropic phase of liquid crystals is described by the rigid ellipsoid diffusion model.     

On the use of a single kinetic parameter in stochastic descriptions of relaxation

Model stochastic processes involving one particle per step transitions (evaluated by Monte-Carlo or theoretically) are often used to describe relaxation. We propose that, lacking further data, the transition probabilities should be defined uniformly with the help of a single kinetic parameter.     

On spectral relaxation in proteins

During the past several years there has been debate about the origins of nonexponential intensity decays of intrinsic tryptophan (trp) fluorescence of proteins, especially for single tryptophan proteins (STP). In this review we summarize the data from diverse sources suggesting that time-dependent spectral relaxation is a ubiquitous feature of protein fluorescence. For most proteins, the observations from numerous laboratories have shown that for trp residues in proteins (1) the mean decay times increase with increasing observation wavelength; (2) decay associated spectra generally show longer decay times for the longer wavelength components; and (3) collisional quenching of proteins usually results in emission spectral shifts to shorter wavelengths. Additional evidence for spectral relaxation comes from the time-resolved emission spectra that usually shows time-dependent shifts to longer wavelengths. These overall observations are consistent with spectral relaxation in proteins occurring on a subnanosecond timescale. These results suggest that spectral relaxation is a significant if not dominant source of nonexponential decay in STP, and should be considered in any interpretation of nonexponential decay of intrinsic protein fluorescence.     

Nonexponential relaxation and fragility in a model system and in supercooled liquids

Among the outstanding problems in the theory of supercooled liquids are the reasons for the rapid increase in their viscosity and relaxation times as the temperature is lowered towards the glass transition temperature Tg, the nonexponential time dependence of the relaxation, and the possible connection between these two properties. The ferromagnetic Potts model on a square latice is a simple system that is found to exhibit these properties. Our calculations show that in this system the connection between them is associated with the dependence on temperature and time of the average environment of the sites. Some of the consequences of this for understanding the behavior of supercooled liquids are discussed.     

On the interpretation of vibrational relaxation measurements

The relative relaxation rates of vibrational level populations following establishment of a Boltzmann vibrational distribution by rapid vibration—vibration energy transfer are shown to depend on the nature and extent of the departure from equilibrium. The only kinetic information obtainable under such conditions is τ, the relaxation time of the vibrational energy. The implications for interpretation of laser-induced vibrational fluorescence measurements are emphasized.